Evolution of deformation and stress during necking in uniaxial tension

Abstract

In this investigation, we study experimentally the evolution of both the deformation and the stress during the necking process of a thin metal sheet subject to uniaxial tension. The deformation over the sample surface is obtained using the optical technique of Digital Image Correlation (DIC), which maps out full-field displacement over a two-dimensional (2D) domain. The stress field associated with the measured deformation is determined using the technique developed by Liu [18], where if the deforming material remains isotropic, the stresses can be computed based on the measured deformation by solving the equation of equilibrium together with appropriate traction boundary conditions. The deformation measurement indicates that after the initiation of the neck the deformation in areas outside the neck is frozen, confirming what Bridgman [2] has speculated, and the deformation within the neck area continues to increase till final failure. There is never a reversal in deformation and, as a result, all material particles in the necking zone only experience softening but not unloading. The results also reveal some unique and interesting patterns of the stress field over the necking zone. Their implications on the analysis and modeling of the necking process are discussed.

Keywords

• Necking
• Uniaxial tension
• Metal sheet
• Stress analysis
• DIC